adding exact gaussian inference

GPy/inference/latent_function_inference/exact_gaussian_inference.py

@@ -0,0 +1,13 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+def exact_gaussian_inference(K, likelihood, Y, Y_metadata=None):
+
+
+    Wi, LW, LWi, W_logdet = pdinv(K + likelhood.covariance(Y, Y_metadata))
+
+    alpha, _ = dpotrs(LW, YYT_factor, lower=1)
+    dL_dK = 0.5 * (tdot(alpha) - Y.shape[1] * Wi)
+
+    log_marginal =  (-0.5 * Y.size * np.log(2.*np.pi) -
+        0.5 * Y.shape[1] * W_logdet + np.sum(np.square(alpha))